English

Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation

Analysis of PDEs 2009-11-24 v1

Abstract

In this work, we consider a spatially homogeneous Kac's equation with a non cutoff cross section. We prove that the weak solution of the Cauchy problem is in the Gevrey class for positive time. This is a Gevrey regularizing effect for non smooth initial datum. The proof relies on the Fourier analysis of Kac's operators and on an exponential type mollifier.

Keywords

Cite

@article{arxiv.0911.4279,
  title  = {Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation},
  author = {Nadia Lekrine and Chao-Jiang Xu},
  journal= {arXiv preprint arXiv:0911.4279},
  year   = {2009}
}